Problem: Simplify the following expression: $t = \dfrac{a^2 - a - 30}{a - 6} $
Explanation: First factor the polynomial in the numerator. $ a^2 - a - 30 = (a - 6)(a + 5) $ So we can rewrite the expression as: $t = \dfrac{(a - 6)(a + 5)}{a - 6} $ We can divide the numerator and denominator by $(a - 6)$ on condition that $a \neq 6$ Therefore $t = a + 5; a \neq 6$